Alfonso Gracia-Saz

I am a postdoctoral fellow with the symplectic geometry group at the Mathematics Department of the University of Toronto. My sponsors here are Lisa Jeffrey, Yael Karshon, Boris Khesin, and Eckhard Meinrenken.
I got my PhD from UC Berkeley under the supervision of Alan Weinstein in 2006, and I spend then a year at Keio University with Yoshiaki Maeda.

My Ph.D. thesis: (pdf)

MAT 135 student, click here.

CONTACT

Email: alfonso (at-sing) math (dot) toronto (dot) edu
Office: 215 Huron St, Office 1023 (10th floor)
Phone: 416-946-3771
Mail address: Mathematics Department, University of Toronto, 40 St George St Room 6290, Toronto ON M5S 2E4, Canada.

PAPERS

Publications

A. Gracia-Saz: The symbol of a function of an operator, Ann. Inst. Fourier 55 (2005) 2257-2284. pdf
M. Cargo, A. Gracia-Saz, R.G. Littlejohn, M.W. Reinsch and P.de M. Rios: Quantum normal forms, Moyal star product and Bohr-Sommerfeld approximation, J. Phys. A: Math. Gen. 38 (2005) 1977-2004. pdf

Preprints

M.Cargo, A. Gracia-Saz, and R. Littlejohn: Multidimensional quantum normal forms, Moyal star product, and torus quantization. arXiv:math-ph/0507032 .

In preparation

A. Gracia-Saz and K.Mackenzie: Duality of n-fold vector bundles.
A. Gracia-Saz and R. Mehta: Lie algebroid vector bundles and the theory of connections.

Here are some surveys I wrote for graduate courses I took with Alan Weistein:

The classification of holonomy groups of affine connections (term paper for Riemannian Geometry, Fall 2003). pdf
On Kontsevich formula for deformation quantization (term paper for Symplectic Geometry, Fall 2002). pdf

Some groups that I have been or am involved with:

Canada/USA Mathcamp, the happiest place on Earth.
Prison University Project, providing immates with access to education.
Iberia-Berkeley, association of Spaniards in Berkeley.
Toronto Country Dancers, contra dancing in Toronto.
Triangle Squares, square dancing in Toronto.
My alma mater.
My other alma mater.
The Sarong Theorem Archive, no explanation needed.